Update apps filtering and styles to show stage and remove advanced mode filters

[timmo001]

Breaking change

Proposed change

• Remove stage filtering in app store
• Add badge for stage, other than stable in installed and store
• Improve styling and inconsistencies between installed and store
• Remove advanced mode filter entirely - not in original task, but based on merged supervisor PRs (Deprecate advanced mode option in addon config supervisor#6614 / Document deprecation of advanced mode in apps developers.home-assistant#2982) should no longer use advanced mode in apps

Screenshots

Installed:

Store:

Type of change

• Dependency upgrade
• Bugfix (non-breaking change which fixes an issue)
• New feature (thank you!)
• Breaking change (fix/feature causing existing functionality to break)
• Code quality improvements to existing code or addition of tests

Additional information

• This PR fixes or closes issue: resolves Make apps stage not affected by advanced mode #30067
• This PR is related to issue or discussion:
• Link to documentation pull request:
• Link to developer documentation pull request:
• Link to backend pull request:

Checklist

• I understand the code I am submitting and can explain how it works.
• The code change is tested and works locally.
• There is no commented out code in this PR.
• I have followed the development checklist
• I have followed the perfect PR recommendations
• Any generated code has been carefully reviewed for correctness and compliance with project standards.

If user exposed functionality or configuration variables are added/changed:

• Documentation added/updated for www.home-assistant.io

To help with the load of incoming pull requests:

• I have reviewed two other open pull requests in this repository.